derivative of-(-2ln(x+3)/(x^3))

Lösung

\frac{d}{d x} (- \frac{- 2 ln ( x ) + 3}{x ^{3}})

\frac{- 6 ln ( x ) + 11}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{- 2 ln ( x ) + 3}{x ^{3}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{- 2 ln ( x ) + 3}{x ^{3}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d x} ( - 2 ln ( x ) + 3 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( - 2 ln ( x ) + 3 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (- 2 ln (x) + 3) = - \frac{2}{x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

= - \frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( - 2 ln ( x ) + 3 )}{( x ^{3} ) ^{2}}

Vereinfache

- \frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( - 2 ln ( x ) + 3 )}{( x ^{3} ) ^{2}} : \frac{- 6 ln ( x ) + 11}{x ^{4}}

= \frac{- 6 ln ( x ) + 11}{x ^{4}}

in v erse l a pl a ce \frac{( 12 s + 3 )}{s ^{2} ( 2 s + 8 )}

\int \frac{1}{- x ^{- 2} + 2 x} d x

y^{^{'}} + \frac{y}{9.33} = 6.429

y^{^{''}} = x^{4}

in v erse l a pl a ce \frac{s}{s + 3}